OFFSET
4,3
COMMENTS
The condition of the selection is also known as "no 3-term arithmetic progressions".
A reflection of a selection is not counted. If reflections are to be counted see A300760.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 4..1000
FORMULA
a(n) = (n^4 - 12*n^3 + 54*n^2 - 88*n)/48 + (n == 1 (mod 2))*(-4*n + 19)/16 + (n == 5 (mod 6))/3 + (n == 2 (mod 6))/3 + (n == 2 (mod 4))/2.
a(n) = (n^4 - 12*n^3 + 54*n^2 - 88*n)/48 + b(n) + c(n), where
b(n) = 0 for n even
b(n) = (-4*n + 19)/16 for n odd
c(n) = 0 for n == 0,1,3,4,7,9 (mod 12)
c(n) = 1/3 for n == 5,8,11 (mod 12)
c(n) = 1/2 for n == 6,10 (mod 12)
c(n) = 5/6 for n == 2 (mod 12).
From Colin Barker, Mar 15 2018: (Start)
G.f.: x^5*(1 + x + 4*x^3 + x^4 + 5*x^5) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).
a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11) for n>14.
(End)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Mar 15 2018
STATUS
approved